MAT 2500 Calculus III (for science and engineering)

Textbook: James Stewart: Calculus: Early Trancendentals (Edition 6e, 2007)
ISBN-10: 049383430  |  ISBN-13: 9780495383437

Chapters 10, 12-16 (parametric equations, vectors, vector functions, partial derivatives, multiple integrals, vector calculus)  edited to streamline material to permit coverage.
Single square brackets [...] indicate optional material;
double square brackets [[...]] indicate omitted material

• 10. Parametric Equations and Polar Coordinates
  • 10.1 Curves Defined By Parametric Equations POSTPONED till after 12.4
  • 10.2 Calculus with Parametric Curves POSTPONED till after 12.4
  • 10.3 Polar Coordinates POSTPONED WITH 15.4, 12.7 TILL JUST BEFORE 15.8
  • [[10.4 Areas and Lengths in Polar Coordinates]]
  • [[10.5 Conic Sections]]
  • [[10.6 Conic Sections in Polar Coordinates]]
• 12. VECTORS AND THE GEOMETRY OF SPACE
  • 12.1. Three-Dimensional Coordinate Systems
  • 12.2 Vectors
  • 12.3 The Dot Product
  • 12.4 The Cross Product
  • 12.5 Equations of Lines and Planes
  • [[12.6 Cylinders and Quadric Surfaces]]
  • 12.7 Cylindrical and Spherical Coordinates POSTPONED TILL JUST BEFORE 15.8
  •  
• 13. VECTOR FUNCTIONS
  • 13.1 Vector Functions and Space Curves
  • 13.2 Derivatives and Integrals of Vector Functions
  • 13.3 Arc Length and Curvature
  • 13.4 Motion in Space: Velocity and Acceleration
  •  
• 14. PARTIAL DERIVATIVES
  • 14.1 Functions of Several Variables
  • [[14.2 Limits and Continuity]] REMARKS ONLY WITH 14.3, 14.4
  • 14.3 Partial Derivatives
  • 14.4 Tangent Planes and Linear Approximations
  • 14.5 The Chain Rule
  • 14.6 Directional Derivatives and the Gradient Vector
  • 14.7 Maximum and Minimum Values
  • 14.8 [[Lagrange Multipliers]]
  •  
• 15. MULTIPLE INTEGRALS
  • 15.1 Double Integrals over Rectangles
  • 15.2 Integrated Integrals
  • 15.3 Double Integrals over General Regions
  • 15.4 Double Integrals in Polar Coordinates POSTPONED TILL JUST BEFORE 15.8
  • 15.5 Applications of Double Integrals
  • [[15.6 Surface Area]]
  • 15.7 Triple Integrals
  • NOW: 10.4, 15.4, 12.7
  • 15.8 Triple Integrals in Cylindrical and Spherical Coordinates
  • [[15.9 Change of Variables in Multiple Integrals]]
  •  
• 16. VECTOR CALCULUS
  • 16.1 Vector Fields
  • 16.2 Line Integrals
  • 16.3 The Fundamental Theorem for Line Integrals
  • 16.4 Green's Theorem
  • 16.5 Curl and Divergence
  • [16.6 Parametric Surfaces and Their Areas]
  • [16.7 Surface Integrals;    15.6 Remarks]
  • [16.8 Stokes' Theorem]
  • [16.9 The Divergence Theorem]
  • [[16.10 Summary]]

Elementary use of MAPLE is a required supporting tool in the entire MAT1500-1505-2500-2705 sequence of Calculus and Differential Equations with Linear Algebra for Science and Engineering majors.

MAPLE Supplementary Text:
A. Belmonte and P. Yasskin, CalcLabs with MAPLE for Stewart's Multivariable Calculus (2003)

Also available (ask your instructor, or go to the website):

• IVS CD included with textbook: some explanatory videos and quizzes, math tutorial software.
• TEC CD included with textbook: Red numbered problem homework hints, Java applets for visualizing concepts.
  To use the homework hints (Fall 2006), if you find that the Java applets on your computer do not run, you must download Java Runtime Environment JRE 6 beta from Sun and install (very quick, only about 50MB, just say yes to license dialog).
   
• Student Solution Manual (all odd problems worked); must be ordered from the publisher
• Stewart Calculus website